Two coherent sources $S_1$ and $S_2$ separated by distance $2\lambda$ emit light of wavelength $\lambda$ in phase as shown in the figure. A circular wire of radius $100\lambda$ is placed in such a way that $S_1{S}_2$ lies in its plane and the mid-point of $S_1{S}_2$ is at the centre of wire. 

(i) Find the angular positions $\theta$ on the wire for which constructive interference takes place. Hence or otherwise find the total number of maxima.

(ii) Find the angular positions $\theta$ (in the first quadrant) on the wire for which intensity reduces to half of its maximum value.

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